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We investigate the influence of dynamical charm quarks on observables thatdepend explicitly on the charm quark fields, like the pseudo-scalar and vectormasses $m_{\eta_c}$ and $m_{J/\psi}$, the hyperfine splitting$(m_{J/\psi}-m_{\eta_c})/m_{\eta_c}$, the charm quark mass and the meson decayconstants. For this purpose, instead of working in full QCD we study asimplified setup. We simulate two theories: $N_f= 0$ QCD and QCD with $N_f= 2$dynamical quarks at the charm mass. The absence of light quarks allows us toreach extremely fine lattice spacings (0.02 fm < a < 0.05 fm) which are crucialfor reliable continuum extrapolations. Our main result is a comparison ofvarious quantities in the continuum limit. For the hyperfine splitting we findthat the effects of a dynamical charm quark are below our statistical precisionof $2\%$.

Comparison between models of QCD with and without dynamical charm quarks